Magnetic field strength that emits waves

[jayayo]

Homework Statement

The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at 2.99GHz, and as they do so they emit 2.99GHz electromagnetic waves. What is the magnetic field strength?

Homework Equations

ƒ=qβ/(2Pi*m)
Thus, B= f*2Pi*m/q

The Attempt at a Solution

I got the question right. It's just I am having a bit difficult grasping why. I thought that because they stated that the electrons also emit 2.99Hz electromagnetic waves, that this would influence the answer. Could someone please explain to me if electrons emitting waves of the same frequency has any influence on this question and the found B value? And also, if not, why?

Thank you so much!

 

[rude man]

The electrons ARE what generate the e-m waves. The frequency is just the electrons' rotational frequency. So I don't know what you mean by ".. the electrons ALSO emit 2.99 GHz electromagnetic waves ...".

The problem just involves equating the Lorentz force with centripetal force which your formula does.

 

[jayayo]

The electrons ARE what generate the e-m waves. The frequency is just the electrons' rotational frequency. So I don't know what you mean by ".. the electrons ALSO emit 2.99 GHz electromagnetic waves ...".

The problem just involves equating the Lorentz force with centripetal force which your formula does.

Hi~
Sorry- pretty stupid of me. I just thought because they purposely added the fact that the electrons also emitted EM waves of the same frequency, maybe this would increase or decrease the value of the magnetic field.
What would change due to the fact that the electrons were emitting EM waves of the same frequency? Energy, right? Anything else?

 

[rude man]

Hi~
Sorry- pretty stupid of me. I just thought because they purposely added the fact that the electrons also emitted EM waves of the same frequency, maybe this would increase or decrease the value of the magnetic field.
What would change due to the fact that the electrons were emitting EM waves of the same frequency? Energy, right? Anything else?

The B field is not affected. Without the electrons there would not be any e-m radiation. If the electrons were present but stationary you would have a static E field on top of the B field but no e-m radiation. Charges have to be accelerated to emit e-m radiation.

E-m radiation carries energy with it. The so-called Poynting vector P indicates the direction of e-m radiation and energy transport. The power flux is P times the area under consideration, expressed as a dot product since both P and area A are vectors, and the units are watts/square meter. So power flow = P*A over any area.

It can be shown that P = E x H.

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[HalfLostAndSearching]

I would like to clarify that the frequency of the emitted electromagnetic waves does not directly influence the calculation of the magnetic field strength. The equation provided is correct and can be used to calculate the magnetic field strength based on the given frequency, charge and mass of the electrons.

However, it is important to note that the frequency of the emitted waves is directly related to the frequency at which the electrons orbit the magnetic field. This means that the frequency of the emitted waves will be the same as the frequency of the electrons' orbit, which in this case is 2.99GHz. This information is helpful in understanding the behavior of the electrons and the resulting electromagnetic waves, but it does not affect the calculation of the magnetic field strength.

In summary, the frequency of the emitted waves is a result of the frequency of the electrons' orbit, but it does not have a direct influence on the calculation of the magnetic field strength.